Find the value of (102) $^{2}$ + (98) $^{2}$ .
$[2 M a r k s]$

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Solution

(102) $^{2}$ can be written as (100+2) $^{2} (0.5 M a r k)$ ,
(98) $^{2}$ can be written as (100-2) $^{2} (0.5 M a r k)$ .
Using the identity $(a + b)^{2} + (a - b)^{2} = 2 (a^{2} + b^{2})$
$(102)^{2} + (98)^{2} = 2 (100^{2} + 2^{2}) = 20008 (1 M a r k)$ .

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